Getting Started
create a list of R packages required
packages <- c('olsrr', 'GWmodel', 'tmap', 'sf', 'corrplot', 'tidyverse', 'ggpubr', 'spdep')
for (p in packages) {
if (!require(p, character.only = T)) {
install.packages(p)
}
library(p, character.only = T)
}
Import geospatial data into r environment
mpsz = st_read(dsn = "data/geospatial", layer = "MP14_SUBZONE_WEB_PL")
Reading layer `MP14_SUBZONE_WEB_PL' from data source
`/Users/pengtaixu/IS415_blog/_posts/2021-10-18-hands-on-exercise-9/data/geospatial'
using driver `ESRI Shapefile'
Simple feature collection with 323 features and 15 fields
Geometry type: MULTIPOLYGON
Dimension: XY
Bounding box: xmin: 2667.538 ymin: 15748.72 xmax: 56396.44 ymax: 50256.33
Projected CRS: SVY21- update CRS information with the correct ESPG code
mpsz_svy21 <- st_transform(mpsz, 3414)Import aspatial data into r environment
condo_resale = read_csv("data/aspatial/Condo_resale_2015.csv")glimpse(condo_resale)Rows: 1,436 Columns: 23 $ LATITUDE <dbl> 1.287145, 1.328698, 1.313727, 1.308563,… $ LONGITUDE <dbl> 103.7802, 103.8123, 103.7971, 103.8247,… $ POSTCODE <dbl> 118635, 288420, 267833, 258380, 467169,… $ SELLING_PRICE <dbl> 3000000, 3880000, 3325000, 4250000, 140… $ AREA_SQM <dbl> 309, 290, 248, 127, 145, 139, 218, 141,… $ AGE <dbl> 30, 32, 33, 7, 28, 22, 24, 24, 27, 31, … $ PROX_CBD <dbl> 7.941259, 6.609797, 6.898000, 4.038861,… $ PROX_CHILDCARE <dbl> 0.16597932, 0.28027246, 0.42922669, 0.3… $ PROX_ELDERLYCARE <dbl> 2.5198118, 1.9333338, 0.5021395, 1.9910… $ PROX_URA_GROWTH_AREA <dbl> 6.618741, 7.505109, 6.463887, 4.906512,… $ PROX_HAWKER_MARKET <dbl> 1.76542207, 0.54507614, 0.37789301, 1.6… $ PROX_KINDERGARTEN <dbl> 0.05835552, 0.61592412, 0.14120309, 0.3… $ PROX_MRT <dbl> 0.5607188, 0.6584461, 0.3053433, 0.6910… $ PROX_PARK <dbl> 1.1710446, 0.1992269, 0.2779886, 0.9832… $ PROX_PRIMARY_SCH <dbl> 1.6340256, 0.9747834, 1.4715016, 1.4546… $ PROX_TOP_PRIMARY_SCH <dbl> 3.3273195, 0.9747834, 1.4715016, 2.3006… $ PROX_SHOPPING_MALL <dbl> 2.2102717, 2.9374279, 1.2256850, 0.3525… $ PROX_SUPERMARKET <dbl> 0.9103958, 0.5900617, 0.4135583, 0.4162… $ PROX_BUS_STOP <dbl> 0.10336166, 0.28673408, 0.28504777, 0.2… $ NO_Of_UNITS <dbl> 18, 20, 27, 30, 30, 31, 32, 32, 32, 32,… $ FAMILY_FRIENDLY <dbl> 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, … $ FREEHOLD <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, … $ LEASEHOLD_99YR <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …- converting aspatial data frame into a sf object
condo_resale.sf <- st_as_sf(condo_resale, coords = c("LONGITUDE", "LATITUDE"), crs=4326) %>% st_transform(crs=3414) head(condo_resale.sf)Simple feature collection with 6 features and 21 fields Geometry type: POINT Dimension: XY Bounding box: xmin: 22085.12 ymin: 29951.54 xmax: 41042.56 ymax: 34546.2 Projected CRS: SVY21 / Singapore TM # A tibble: 6 × 22 POSTCODE SELLING_PRICE AREA_SQM AGE PROX_CBD PROX_CHILDCARE <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> 1 118635 3000000 309 30 7.94 0.166 2 288420 3880000 290 32 6.61 0.280 3 267833 3325000 248 33 6.90 0.429 4 258380 4250000 127 7 4.04 0.395 5 467169 1400000 145 28 11.8 0.119 6 466472 1320000 139 22 10.3 0.125 # … with 16 more variables: PROX_ELDERLYCARE <dbl>, # PROX_URA_GROWTH_AREA <dbl>, PROX_HAWKER_MARKET <dbl>, # PROX_KINDERGARTEN <dbl>, PROX_MRT <dbl>, PROX_PARK <dbl>, # PROX_PRIMARY_SCH <dbl>, PROX_TOP_PRIMARY_SCH <dbl>, # PROX_SHOPPING_MALL <dbl>, PROX_SUPERMARKET <dbl>, # PROX_BUS_STOP <dbl>, NO_Of_UNITS <dbl>, FAMILY_FRIENDLY <dbl>, # FREEHOLD <dbl>, LEASEHOLD_99YR <dbl>, geometry <POINT [m]>EDA
AREA_SQM <- ggplot(data=condo_resale.sf, aes(x= `AREA_SQM`)) + geom_histogram(bins=20, color="black", fill="light blue") AGE <- ggplot(data=condo_resale.sf, aes(x= `AGE`)) + geom_histogram(bins=20, color="black", fill="light blue") PROX_CBD <- ggplot(data=condo_resale.sf, aes(x= `PROX_CBD`)) + geom_histogram(bins=20, color="black", fill="light blue") PROX_CHILDCARE <- ggplot(data=condo_resale.sf, aes(x= `PROX_CHILDCARE`)) + geom_histogram(bins=20, color="black", fill="light blue") PROX_ELDERLYCARE <- ggplot(data=condo_resale.sf, aes(x= `PROX_ELDERLYCARE`)) + geom_histogram(bins=20, color="black", fill="light blue") PROX_URA_GROWTH_AREA <- ggplot(data=condo_resale.sf, aes(x= `PROX_URA_GROWTH_AREA`)) + geom_histogram(bins=20, color="black", fill="light blue") PROX_HAWKER_MARKET <- ggplot(data=condo_resale.sf, aes(x= `PROX_HAWKER_MARKET`)) + geom_histogram(bins=20, color="black", fill="light blue") PROX_KINDERGARTEN <- ggplot(data=condo_resale.sf, aes(x= `PROX_KINDERGARTEN`)) + geom_histogram(bins=20, color="black", fill="light blue") PROX_MRT <- ggplot(data=condo_resale.sf, aes(x= `PROX_MRT`)) + geom_histogram(bins=20, color="black", fill="light blue") PROX_PARK <- ggplot(data=condo_resale.sf, aes(x= `PROX_PARK`)) + geom_histogram(bins=20, color="black", fill="light blue") PROX_PRIMARY_SCH <- ggplot(data=condo_resale.sf, aes(x= `PROX_PRIMARY_SCH`)) + geom_histogram(bins=20, color="black", fill="light blue") PROX_TOP_PRIMARY_SCH <- ggplot(data=condo_resale.sf, aes(x= `PROX_TOP_PRIMARY_SCH`)) + geom_histogram(bins=20, color="black", fill="light blue") ggarrange(AREA_SQM, AGE, PROX_CBD, PROX_CHILDCARE, PROX_ELDERLYCARE, PROX_URA_GROWTH_AREA, PROX_HAWKER_MARKET, PROX_KINDERGARTEN, PROX_MRT, PROX_PARK, PROX_PRIMARY_SCH, PROX_TOP_PRIMARY_SCH, ncol = 3, nrow = 4)
Drawing Statistical Point Map
tmap_mode("view") tm_shape(mpsz_svy21)+ tm_polygons() + tm_shape(condo_resale.sf) + tm_dots(col = "SELLING_PRICE", alpha = 0.6, style="quantile") + tmap_options(check.and.fix = TRUE) + tm_view(set.zoom.limits = c(11,14))tmap_mode("plot")simple linear regression
Call: lm(formula = SELLING_PRICE ~ AREA_SQM, data = condo_resale.sf) Residuals: Min 1Q Median 3Q Max -3695815 -391764 -87517 258900 13503875 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -258121.1 63517.2 -4.064 5.09e-05 *** AREA_SQM 14719.0 428.1 34.381 < 2e-16 *** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 942700 on 1434 degrees of freedom Multiple R-squared: 0.4518, Adjusted R-squared: 0.4515 F-statistic: 1182 on 1 and 1434 DF, p-value: < 2.2e-16- refer to scatter plot to check linearity
ggplot(data=condo_resale.sf, aes(x=`AREA_SQM`, y=`SELLING_PRICE`)) + geom_point() + geom_smooth(method = lm)
multiple linear regression
- EDA
corrplot(cor(condo_resale[, 5:23]), diag = FALSE, order = "AOE", tl.pos = "td", tl.cex = 0.5, method = "number", type = "upper")
- regression
condo.mlr <- lm(formula = SELLING_PRICE ~ AREA_SQM + AGE + PROX_CBD + PROX_CHILDCARE + PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA + PROX_HAWKER_MARKET + PROX_KINDERGARTEN + PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH + PROX_TOP_PRIMARY_SCH + PROX_SHOPPING_MALL + PROX_SUPERMARKET + PROX_BUS_STOP + NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD, data=condo_resale.sf) summary(condo.mlr)Call: lm(formula = SELLING_PRICE ~ AREA_SQM + AGE + PROX_CBD + PROX_CHILDCARE + PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA + PROX_HAWKER_MARKET + PROX_KINDERGARTEN + PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH + PROX_TOP_PRIMARY_SCH + PROX_SHOPPING_MALL + PROX_SUPERMARKET + PROX_BUS_STOP + NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD, data = condo_resale.sf) Residuals: Min 1Q Median 3Q Max -3475964 -293923 -23069 241043 12260381 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 481728.40 121441.01 3.967 7.65e-05 *** AREA_SQM 12708.32 369.59 34.385 < 2e-16 *** AGE -24440.82 2763.16 -8.845 < 2e-16 *** PROX_CBD -78669.78 6768.97 -11.622 < 2e-16 *** PROX_CHILDCARE -351617.91 109467.25 -3.212 0.00135 ** PROX_ELDERLYCARE 171029.42 42110.51 4.061 5.14e-05 *** PROX_URA_GROWTH_AREA 38474.53 12523.57 3.072 0.00217 ** PROX_HAWKER_MARKET 23746.10 29299.76 0.810 0.41782 PROX_KINDERGARTEN 147468.99 82668.87 1.784 0.07466 . PROX_MRT -314599.68 57947.44 -5.429 6.66e-08 *** PROX_PARK 563280.50 66551.68 8.464 < 2e-16 *** PROX_PRIMARY_SCH 180186.08 65237.95 2.762 0.00582 ** PROX_TOP_PRIMARY_SCH 2280.04 20410.43 0.112 0.91107 PROX_SHOPPING_MALL -206604.06 42840.60 -4.823 1.57e-06 *** PROX_SUPERMARKET -44991.80 77082.64 -0.584 0.55953 PROX_BUS_STOP 683121.35 138353.28 4.938 8.85e-07 *** NO_Of_UNITS -231.18 89.03 -2.597 0.00951 ** FAMILY_FRIENDLY 140340.77 47020.55 2.985 0.00289 ** FREEHOLD 359913.01 49220.22 7.312 4.38e-13 *** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 755800 on 1417 degrees of freedom Multiple R-squared: 0.6518, Adjusted R-squared: 0.6474 F-statistic: 147.4 on 18 and 1417 DF, p-value: < 2.2e-16checks on linear regression assumptions
condo.mlr1 <- lm(formula = SELLING_PRICE ~ AREA_SQM + AGE + PROX_CBD + PROX_CHILDCARE + PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA + PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH + PROX_SHOPPING_MALL + PROX_BUS_STOP + NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD, data=condo_resale.sf) ols_regress(condo.mlr1)Model Summary ------------------------------------------------------------------------ R 0.807 RMSE 755957.289 R-Squared 0.651 Coef. Var 43.168 Adj. R-Squared 0.647 MSE 571471422208.591 Pred R-Squared 0.638 MAE 414819.628 ------------------------------------------------------------------------ RMSE: Root Mean Square Error MSE: Mean Square Error MAE: Mean Absolute Error ANOVA -------------------------------------------------------------------------------- Sum of Squares DF Mean Square F Sig. -------------------------------------------------------------------------------- Regression 1.512586e+15 14 1.080418e+14 189.059 0.0000 Residual 8.120609e+14 1421 571471422208.591 Total 2.324647e+15 1435 -------------------------------------------------------------------------------- Parameter Estimates ----------------------------------------------------------------------------------------------------------------- model Beta Std. Error Std. Beta t Sig lower upper ----------------------------------------------------------------------------------------------------------------- (Intercept) 527633.222 108183.223 4.877 0.000 315417.244 739849.200 AREA_SQM 12777.523 367.479 0.584 34.771 0.000 12056.663 13498.382 AGE -24687.739 2754.845 -0.167 -8.962 0.000 -30091.739 -19283.740 PROX_CBD -77131.323 5763.125 -0.263 -13.384 0.000 -88436.469 -65826.176 PROX_CHILDCARE -318472.751 107959.512 -0.084 -2.950 0.003 -530249.889 -106695.613 PROX_ELDERLYCARE 185575.623 39901.864 0.090 4.651 0.000 107302.737 263848.510 PROX_URA_GROWTH_AREA 39163.254 11754.829 0.060 3.332 0.001 16104.571 62221.936 PROX_MRT -294745.107 56916.367 -0.112 -5.179 0.000 -406394.234 -183095.980 PROX_PARK 570504.807 65507.029 0.150 8.709 0.000 442003.938 699005.677 PROX_PRIMARY_SCH 159856.136 60234.599 0.062 2.654 0.008 41697.849 278014.424 PROX_SHOPPING_MALL -220947.251 36561.832 -0.115 -6.043 0.000 -292668.213 -149226.288 PROX_BUS_STOP 682482.221 134513.243 0.134 5.074 0.000 418616.359 946348.082 NO_Of_UNITS -245.480 87.947 -0.053 -2.791 0.005 -418.000 -72.961 FAMILY_FRIENDLY 146307.576 46893.021 0.057 3.120 0.002 54320.593 238294.560 FREEHOLD 350599.812 48506.485 0.136 7.228 0.000 255447.802 445751.821 ------------------------------------------------------------------------------------------------------------------ multicolinearity
ols_vif_tol(condo.mlr1)Variables Tolerance VIF 1 AREA_SQM 0.8728554 1.145665 2 AGE 0.7071275 1.414172 3 PROX_CBD 0.6356147 1.573280 4 PROX_CHILDCARE 0.3066019 3.261559 5 PROX_ELDERLYCARE 0.6598479 1.515501 6 PROX_URA_GROWTH_AREA 0.7510311 1.331503 7 PROX_MRT 0.5236090 1.909822 8 PROX_PARK 0.8279261 1.207837 9 PROX_PRIMARY_SCH 0.4524628 2.210126 10 PROX_SHOPPING_MALL 0.6738795 1.483945 11 PROX_BUS_STOP 0.3514118 2.845664 12 NO_Of_UNITS 0.6901036 1.449058 13 FAMILY_FRIENDLY 0.7244157 1.380423 14 FREEHOLD 0.6931163 1.442759- normality
ols_plot_resid_hist(condo.mlr1)
ols_test_normality(condo.mlr1)----------------------------------------------- Test Statistic pvalue ----------------------------------------------- Shapiro-Wilk 0.6856 0.0000 Kolmogorov-Smirnov 0.1366 0.0000 Cramer-von Mises 121.0768 0.0000 Anderson-Darling 67.9551 0.0000 ------------------------------------------------ autocorrelation
condo_resale.res.sf <- cbind(condo_resale.sf, condo.mlr1$residuals) %>% rename(`MLR_RES` = `condo.mlr1.residuals`) condo_resale.sp <- as_Spatial(condo_resale.res.sf) nb <- dnearneigh(coordinates(condo_resale.sp), 0, 1500, longlat = FALSE) nb_lw <- nb2listw(nb, style = 'W') lm.morantest(condo.mlr1, nb_lw)Global Moran I for regression residuals data: model: lm(formula = SELLING_PRICE ~ AREA_SQM + AGE + PROX_CBD + PROX_CHILDCARE + PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA + PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH + PROX_SHOPPING_MALL + PROX_BUS_STOP + NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD, data = condo_resale.sf) weights: nb_lw Moran I statistic standard deviate = 24.366, p-value < 2.2e-16 alternative hypothesis: greater sample estimates: Observed Moran I Expectation Variance 1.438876e-01 -5.487594e-03 3.758259e-05Building Hedonic Pricing Models using GWmodel
- fixed bandwith
bw.fixed <- bw.gwr(formula = SELLING_PRICE ~ AREA_SQM + AGE + PROX_CBD + PROX_CHILDCARE + PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA + PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH + PROX_SHOPPING_MALL + PROX_BUS_STOP + NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD, data=condo_resale.sp, approach="CV", kernel="gaussian", adaptive=FALSE, longlat=FALSE)Fixed bandwidth: 17660.96 CV score: 8.259118e+14 Fixed bandwidth: 10917.26 CV score: 7.970454e+14 Fixed bandwidth: 6749.419 CV score: 7.273273e+14 Fixed bandwidth: 4173.553 CV score: 6.300006e+14 Fixed bandwidth: 2581.58 CV score: 5.404958e+14 Fixed bandwidth: 1597.687 CV score: 4.857515e+14 Fixed bandwidth: 989.6077 CV score: 4.722431e+14 Fixed bandwidth: 613.7939 CV score: 1.37828e+16 Fixed bandwidth: 1221.873 CV score: 4.778717e+14 Fixed bandwidth: 846.0596 CV score: 4.791629e+14 Fixed bandwidth: 1078.325 CV score: 4.751406e+14 Fixed bandwidth: 934.7772 CV score: 4.72518e+14 Fixed bandwidth: 1023.495 CV score: 4.730305e+14 Fixed bandwidth: 968.6643 CV score: 4.721317e+14 Fixed bandwidth: 955.7206 CV score: 4.722072e+14 Fixed bandwidth: 976.6639 CV score: 4.721387e+14 Fixed bandwidth: 963.7202 CV score: 4.721484e+14 Fixed bandwidth: 971.7199 CV score: 4.721293e+14 Fixed bandwidth: 973.6083 CV score: 4.721309e+14 Fixed bandwidth: 970.5527 CV score: 4.721295e+14 Fixed bandwidth: 972.4412 CV score: 4.721296e+14 Fixed bandwidth: 971.2741 CV score: 4.721292e+14 Fixed bandwidth: 970.9985 CV score: 4.721293e+14 Fixed bandwidth: 971.4443 CV score: 4.721292e+14 Fixed bandwidth: 971.5496 CV score: 4.721293e+14 Fixed bandwidth: 971.3793 CV score: 4.721292e+14 Fixed bandwidth: 971.3391 CV score: 4.721292e+14 Fixed bandwidth: 971.3143 CV score: 4.721292e+14 Fixed bandwidth: 971.3545 CV score: 4.721292e+14 Fixed bandwidth: 971.3296 CV score: 4.721292e+14 Fixed bandwidth: 971.345 CV score: 4.721292e+14 Fixed bandwidth: 971.3355 CV score: 4.721292e+14 Fixed bandwidth: 971.3413 CV score: 4.721292e+14 Fixed bandwidth: 971.3377 CV score: 4.721292e+14 Fixed bandwidth: 971.34 CV score: 4.721292e+14 Fixed bandwidth: 971.3405 CV score: 4.721292e+14 Fixed bandwidth: 971.3408 CV score: 4.721292e+14 Fixed bandwidth: 971.341 CV score: 4.721292e+14 Fixed bandwidth: 971.3407 CV score: 4.721292e+14 Fixed bandwidth: 971.3409 CV score: 4.721292e+14 Fixed bandwidth: 971.3408 CV score: 4.721292e+14 Fixed bandwidth: 971.3408 CV score: 4.721292e+14gwr.fixed <- gwr.basic(formula = SELLING_PRICE ~ AREA_SQM + AGE + PROX_CBD + PROX_CHILDCARE + PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA + PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH + PROX_SHOPPING_MALL + PROX_BUS_STOP + NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD, data=condo_resale.sp, bw=bw.fixed, kernel = 'gaussian', longlat = FALSE) gwr.fixed*********************************************************************** * Package GWmodel * *********************************************************************** Program starts at: 2021-10-18 10:43:09 Call: gwr.basic(formula = SELLING_PRICE ~ AREA_SQM + AGE + PROX_CBD + PROX_CHILDCARE + PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA + PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH + PROX_SHOPPING_MALL + PROX_BUS_STOP + NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD, data = condo_resale.sp, bw = bw.fixed, kernel = "gaussian", longlat = FALSE) Dependent (y) variable: SELLING_PRICE Independent variables: AREA_SQM AGE PROX_CBD PROX_CHILDCARE PROX_ELDERLYCARE PROX_URA_GROWTH_AREA PROX_MRT PROX_PARK PROX_PRIMARY_SCH PROX_SHOPPING_MALL PROX_BUS_STOP NO_Of_UNITS FAMILY_FRIENDLY FREEHOLD Number of data points: 1436 *********************************************************************** * Results of Global Regression * *********************************************************************** Call: lm(formula = formula, data = data) Residuals: Min 1Q Median 3Q Max -3470778 -298119 -23481 248917 12234210 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 527633.22 108183.22 4.877 1.20e-06 *** AREA_SQM 12777.52 367.48 34.771 < 2e-16 *** AGE -24687.74 2754.84 -8.962 < 2e-16 *** PROX_CBD -77131.32 5763.12 -13.384 < 2e-16 *** PROX_CHILDCARE -318472.75 107959.51 -2.950 0.003231 ** PROX_ELDERLYCARE 185575.62 39901.86 4.651 3.61e-06 *** PROX_URA_GROWTH_AREA 39163.25 11754.83 3.332 0.000885 *** PROX_MRT -294745.11 56916.37 -5.179 2.56e-07 *** PROX_PARK 570504.81 65507.03 8.709 < 2e-16 *** PROX_PRIMARY_SCH 159856.14 60234.60 2.654 0.008046 ** PROX_SHOPPING_MALL -220947.25 36561.83 -6.043 1.93e-09 *** PROX_BUS_STOP 682482.22 134513.24 5.074 4.42e-07 *** NO_Of_UNITS -245.48 87.95 -2.791 0.005321 ** FAMILY_FRIENDLY 146307.58 46893.02 3.120 0.001845 ** FREEHOLD 350599.81 48506.48 7.228 7.98e-13 *** ---Significance stars Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 756000 on 1421 degrees of freedom Multiple R-squared: 0.6507 Adjusted R-squared: 0.6472 F-statistic: 189.1 on 14 and 1421 DF, p-value: < 2.2e-16 ***Extra Diagnostic information Residual sum of squares: 8.120609e+14 Sigma(hat): 752522.9 AIC: 42966.76 AICc: 42967.14 BIC: 41731.39 *********************************************************************** * Results of Geographically Weighted Regression * *********************************************************************** *********************Model calibration information********************* Kernel function: gaussian Fixed bandwidth: 971.3408 Regression points: the same locations as observations are used. Distance metric: Euclidean distance metric is used. ****************Summary of GWR coefficient estimates:****************** Min. 1st Qu. Median Intercept -3.5988e+07 -5.1998e+05 7.6780e+05 AREA_SQM 1.0003e+03 5.2758e+03 7.4740e+03 AGE -1.3475e+05 -2.0813e+04 -8.6260e+03 PROX_CBD -7.7047e+07 -2.3608e+05 -8.3600e+04 PROX_CHILDCARE -6.0097e+06 -3.3667e+05 -9.7425e+04 PROX_ELDERLYCARE -3.5000e+06 -1.5970e+05 3.1971e+04 PROX_URA_GROWTH_AREA -3.0170e+06 -8.2013e+04 7.0749e+04 PROX_MRT -3.5282e+06 -6.5836e+05 -1.8833e+05 PROX_PARK -1.2062e+06 -2.1732e+05 3.5383e+04 PROX_PRIMARY_SCH -2.2695e+07 -1.7066e+05 4.8472e+04 PROX_SHOPPING_MALL -7.2585e+06 -1.6684e+05 -1.0517e+04 PROX_BUS_STOP -1.4676e+06 -4.5206e+04 3.7601e+05 NO_Of_UNITS -1.3170e+03 -2.4822e+02 -3.0846e+01 FAMILY_FRIENDLY -2.2749e+06 -1.1140e+05 7.6214e+03 FREEHOLD -9.2067e+06 3.8073e+04 1.5169e+05 3rd Qu. Max. Intercept 1.7412e+06 112793007 AREA_SQM 1.2301e+04 21575 AGE -3.7784e+03 434200 PROX_CBD 3.4645e+04 2704591 PROX_CHILDCARE 2.9008e+05 1654088 PROX_ELDERLYCARE 1.9577e+05 38867786 PROX_URA_GROWTH_AREA 2.2612e+05 78515685 PROX_MRT 3.6922e+04 3124310 PROX_PARK 4.1335e+05 18122416 PROX_PRIMARY_SCH 5.1555e+05 4637495 PROX_SHOPPING_MALL 1.5923e+05 1529951 PROX_BUS_STOP 1.1664e+06 11342166 NO_Of_UNITS 2.5496e+02 12907 FAMILY_FRIENDLY 1.6107e+05 1720744 FREEHOLD 3.7528e+05 6073633 ************************Diagnostic information************************* Number of data points: 1436 Effective number of parameters (2trace(S) - trace(S'S)): 438.3803 Effective degrees of freedom (n-2trace(S) + trace(S'S)): 997.6197 AICc (GWR book, Fotheringham, et al. 2002, p. 61, eq 2.33): 42263.61 AIC (GWR book, Fotheringham, et al. 2002,GWR p. 96, eq. 4.22): 41632.36 BIC (GWR book, Fotheringham, et al. 2002,GWR p. 61, eq. 2.34): 42515.71 Residual sum of squares: 2.534071e+14 R-square value: 0.8909911 Adjusted R-square value: 0.8430417 *********************************************************************** Program stops at: 2021-10-18 10:43:10- adaptive
bw.adaptive <- bw.gwr(formula = SELLING_PRICE ~ AREA_SQM + AGE + PROX_CBD + PROX_CHILDCARE + PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA + PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH + PROX_SHOPPING_MALL + PROX_BUS_STOP + NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD, data=condo_resale.sp, approach="CV", kernel="gaussian", adaptive=TRUE, longlat=FALSE)Adaptive bandwidth: 895 CV score: 7.952401e+14 Adaptive bandwidth: 561 CV score: 7.667364e+14 Adaptive bandwidth: 354 CV score: 6.953454e+14 Adaptive bandwidth: 226 CV score: 6.15223e+14 Adaptive bandwidth: 147 CV score: 5.674373e+14 Adaptive bandwidth: 98 CV score: 5.426745e+14 Adaptive bandwidth: 68 CV score: 5.168117e+14 Adaptive bandwidth: 49 CV score: 4.859631e+14 Adaptive bandwidth: 37 CV score: 4.646518e+14 Adaptive bandwidth: 30 CV score: 4.422088e+14 Adaptive bandwidth: 25 CV score: 4.430816e+14 Adaptive bandwidth: 32 CV score: 4.505602e+14 Adaptive bandwidth: 27 CV score: 4.462172e+14 Adaptive bandwidth: 30 CV score: 4.422088e+14gwr.adaptive <- gwr.basic(formula = SELLING_PRICE ~ AREA_SQM + AGE + PROX_CBD + PROX_CHILDCARE + PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA + PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH + PROX_SHOPPING_MALL + PROX_BUS_STOP + NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD, data=condo_resale.sp, bw=bw.adaptive, kernel = 'gaussian', adaptive=TRUE, longlat = FALSE) gwr.adaptive*********************************************************************** * Package GWmodel * *********************************************************************** Program starts at: 2021-10-18 10:43:17 Call: gwr.basic(formula = SELLING_PRICE ~ AREA_SQM + AGE + PROX_CBD + PROX_CHILDCARE + PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA + PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH + PROX_SHOPPING_MALL + PROX_BUS_STOP + NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD, data = condo_resale.sp, bw = bw.adaptive, kernel = "gaussian", adaptive = TRUE, longlat = FALSE) Dependent (y) variable: SELLING_PRICE Independent variables: AREA_SQM AGE PROX_CBD PROX_CHILDCARE PROX_ELDERLYCARE PROX_URA_GROWTH_AREA PROX_MRT PROX_PARK PROX_PRIMARY_SCH PROX_SHOPPING_MALL PROX_BUS_STOP NO_Of_UNITS FAMILY_FRIENDLY FREEHOLD Number of data points: 1436 *********************************************************************** * Results of Global Regression * *********************************************************************** Call: lm(formula = formula, data = data) Residuals: Min 1Q Median 3Q Max -3470778 -298119 -23481 248917 12234210 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 527633.22 108183.22 4.877 1.20e-06 *** AREA_SQM 12777.52 367.48 34.771 < 2e-16 *** AGE -24687.74 2754.84 -8.962 < 2e-16 *** PROX_CBD -77131.32 5763.12 -13.384 < 2e-16 *** PROX_CHILDCARE -318472.75 107959.51 -2.950 0.003231 ** PROX_ELDERLYCARE 185575.62 39901.86 4.651 3.61e-06 *** PROX_URA_GROWTH_AREA 39163.25 11754.83 3.332 0.000885 *** PROX_MRT -294745.11 56916.37 -5.179 2.56e-07 *** PROX_PARK 570504.81 65507.03 8.709 < 2e-16 *** PROX_PRIMARY_SCH 159856.14 60234.60 2.654 0.008046 ** PROX_SHOPPING_MALL -220947.25 36561.83 -6.043 1.93e-09 *** PROX_BUS_STOP 682482.22 134513.24 5.074 4.42e-07 *** NO_Of_UNITS -245.48 87.95 -2.791 0.005321 ** FAMILY_FRIENDLY 146307.58 46893.02 3.120 0.001845 ** FREEHOLD 350599.81 48506.48 7.228 7.98e-13 *** ---Significance stars Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 756000 on 1421 degrees of freedom Multiple R-squared: 0.6507 Adjusted R-squared: 0.6472 F-statistic: 189.1 on 14 and 1421 DF, p-value: < 2.2e-16 ***Extra Diagnostic information Residual sum of squares: 8.120609e+14 Sigma(hat): 752522.9 AIC: 42966.76 AICc: 42967.14 BIC: 41731.39 *********************************************************************** * Results of Geographically Weighted Regression * *********************************************************************** *********************Model calibration information********************* Kernel function: gaussian Adaptive bandwidth: 30 (number of nearest neighbours) Regression points: the same locations as observations are used. Distance metric: Euclidean distance metric is used. ****************Summary of GWR coefficient estimates:****************** Min. 1st Qu. Median Intercept -1.3487e+08 -2.4669e+05 7.7928e+05 AREA_SQM 3.3188e+03 5.6285e+03 7.7825e+03 AGE -9.6746e+04 -2.9288e+04 -1.4043e+04 PROX_CBD -2.5330e+06 -1.6256e+05 -7.7242e+04 PROX_CHILDCARE -1.2790e+06 -2.0175e+05 8.7158e+03 PROX_ELDERLYCARE -1.6212e+06 -9.2050e+04 6.1029e+04 PROX_URA_GROWTH_AREA -7.2686e+06 -3.0350e+04 4.5869e+04 PROX_MRT -4.3781e+07 -6.7282e+05 -2.2115e+05 PROX_PARK -2.9020e+06 -1.6782e+05 1.1601e+05 PROX_PRIMARY_SCH -8.6418e+05 -1.6627e+05 -7.7853e+03 PROX_SHOPPING_MALL -1.8272e+06 -1.3175e+05 -1.4049e+04 PROX_BUS_STOP -2.0579e+06 -7.1461e+04 4.1104e+05 NO_Of_UNITS -2.1993e+03 -2.3685e+02 -3.4699e+01 FAMILY_FRIENDLY -5.9879e+05 -5.0927e+04 2.6173e+04 FREEHOLD -1.6340e+05 4.0765e+04 1.9023e+05 3rd Qu. Max. Intercept 1.6194e+06 18758355 AREA_SQM 1.2738e+04 23064 AGE -5.6119e+03 13303 PROX_CBD 2.6624e+03 11346650 PROX_CHILDCARE 3.7778e+05 2892127 PROX_ELDERLYCARE 2.8184e+05 2465671 PROX_URA_GROWTH_AREA 2.4613e+05 7384059 PROX_MRT -7.4593e+04 1186242 PROX_PARK 4.6572e+05 2588497 PROX_PRIMARY_SCH 4.3222e+05 3381462 PROX_SHOPPING_MALL 1.3799e+05 38038564 PROX_BUS_STOP 1.2071e+06 12081592 NO_Of_UNITS 1.1657e+02 1010 FAMILY_FRIENDLY 2.2481e+05 2072414 FREEHOLD 3.7960e+05 1813995 ************************Diagnostic information************************* Number of data points: 1436 Effective number of parameters (2trace(S) - trace(S'S)): 350.3088 Effective degrees of freedom (n-2trace(S) + trace(S'S)): 1085.691 AICc (GWR book, Fotheringham, et al. 2002, p. 61, eq 2.33): 41982.22 AIC (GWR book, Fotheringham, et al. 2002,GWR p. 96, eq. 4.22): 41546.74 BIC (GWR book, Fotheringham, et al. 2002,GWR p. 61, eq. 2.34): 41914.08 Residual sum of squares: 2.528227e+14 R-square value: 0.8912425 Adjusted R-square value: 0.8561185 *********************************************************************** Program stops at: 2021-10-18 10:43:18Visualisig local R2
condo_resale.sf.adaptive <- st_as_sf(gwr.adaptive$SDF) %>% st_transform(crs=3414) condo_resale.sf.adaptive.svy21 <- st_transform(condo_resale.sf.adaptive, 3414) gwr.adaptive.output <- as.data.frame(gwr.adaptive$SDF) condo_resale.sf.adaptive <- cbind(condo_resale.res.sf, as.matrix(gwr.adaptive.output)) tmap_mode("view") tm_shape(mpsz_svy21)+ tm_polygons(alpha = 0.1) + tm_shape(condo_resale.sf.adaptive) + tm_dots(col = "Local_R2", border.col = "gray60", border.lwd = 1) + tm_view(set.zoom.limits = c(11,14))- By URA planning region
tm_shape(mpsz_svy21[mpsz_svy21$REGION_N=="CENTRAL REGION", ])+ tm_polygons()+ tm_shape(condo_resale.sf.adaptive) + tm_bubbles(col = "Local_R2", size = 0.15, border.col = "gray60", border.lwd = 1)Distill is a publication format for scientific and technical writing, native to the web.
Learn more about using Distill at https://rstudio.github.io/distill.
- By URA planning region
- adaptive
- fixed bandwith
- autocorrelation
- normality
- multicolinearity
- regression
- EDA
- refer to scatter plot to check linearity
- converting aspatial data frame into a sf object